## Central Limit Theorem

A nice illustration of the Central Limit Theorem by convolution.

**in R:**

`Heaviside <- function(x) { ifelse(x>0,1,0) }`

HH <- convolve( Heaviside(x), rev(Heaviside(x)), type = "open" )

HHHH <- convolve(HH, rev(HH), type = "open" )

HHHHHHHH <- convolve(HHHH, rev(HHHH), type = "open" )

etc.

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What I really like about this demonstration is that it’s not a proof, rather an experiment carried out on a computer.

This empiricism is especially cool since the Bell Curve, 80/20 Rule, etc, have become such a religion.

**NERD NOTE:** Which weapon is better, a 1d10 longsword, or a 2d4 oaken staff? Typically the damage is written as 1-10 longsword and 2-8 quarterstaff. However, these ranges disregard the greater likelihood of the quarterstaff scoring 4,5,6 damage than 1,2,7,8. The longsword’s distribution 1d10 ~Uniform[1,10], while 2d4 looks like a Λ. To see this another way, think of the combinatorics.